A savings account can be considered similar to a checking account, although a better name to describe a savings account would be a "limited checking account." The reason for this name being that with a savings account, one can usually deposit and withdraw money as they would with a checking account, but the number of withdrawals and deposits may be limited. The primary purpose of a savings account can be found in the name, it is a "savings" account, meaning that it is supposed to help an individual save money up for whatever reason. A lot of people will choose to have a savings account as well as a checking account so that they can manage their money and save a portion of it as well.
Another popular type of account that helps the term, "Put your money to work for you," come true is called a money-market account. A money-market account is basically an account that pays a significantly higher rate of interest on the money that is in an individual's account. However, a money-market account usually requires that a much higher minimum balance be kept in the bank account before interest can be earned.
The three types of accounts listed above are extremely common, but they are not the only ones. There are CDs (Certificates of Deposit) which is basically when a person deposits a certain amount of money and agrees to leave it in the bank for a specific timeframe; interest will be paid on this amount, causing it to grow until it is able to be withdrawn. More research on the different types of banking accounts on the web, simply use a popular search engine and you should find plenty of useful information.